A merchant blends tea that sells for $5.00 a pound with tea that sells for $3.00 a pound to produce 80 lb of a mixture that sells for $3.75 a pound. How many pounds of each type of tea does the merchant use in the blend?
amount of the $5.00 tea ---- x pounds
amount of the $3.00 tea ---- 80-x
solve for x
5x + 3(80-x) = 80(3.75)
To solve this problem, we can use a system of equations. Let's assume the merchant uses x pounds of tea that sells for $5.00 a pound, and y pounds of tea that sells for $3.00 a pound.
The first equation we can write is for the total weight of the mixture:
x + y = 80. (Equation 1)
The second equation can be written for the total cost of the mixture:
(5x + 3y) / 80 = 3.75. (Equation 2)
Now, let's solve the system of equations.
From Equation 1, we can isolate y:
y = 80 - x.
Substituting this value of y into Equation 2, we have:
(5x + 3(80 - x)) / 80 = 3.75.
Simplifying further:
(5x + 240 - 3x) / 80 = 3.75,
(2x + 240) / 80 = 3.75,
2x + 240 = 3.75 * 80,
2x + 240 = 300.
Subtracting 240 from both sides:
2x = 300 - 240,
2x = 60.
Dividing both sides by 2:
x = 60 / 2,
x = 30.
Now, substitute this value of x back into Equation 1 to solve for y:
30 + y = 80,
y = 80 - 30,
y = 50.
So, the merchant uses 30 pounds of tea that sells for $5.00 a pound and 50 pounds of tea that sells for $3.00 a pound in the blend.